The equations derived in Section 3.7 are based on the assumption that termination occurs exclusively by either disproportionation or combination. This is usually not the case; some pr0portion of each is more common. If as equals the fraction of chains for which termination occurs by disproportionation, it can be shown that 1 2 2* a+( a)_ a N: n _ lp lp lp and Nw_43aap+2p N11 (2 a? From measurements of NJ and NW/Ml it is possible in principle to evaluate a and p. May and Smith)k has done this for a number of polystyrene samples. A selection of their data for which this approach seems feasible is presented below. Since p is very close to unity, it is adequate to assume this value and evaluate a from NW/Nn and then use the value of at so obtained to evaluate a better value of p from N. Na Nw/Nn 1 129 1.60 924 1.67 674 1.73 609 1 .74. Derive the two equations given in the previous problem. It may be helpful to recognize that for any distribution taken as a whole, w. = ixi/Nn.